Measure the volume contained in this cylinder.

Answer:

You don't need calculus for this one.
The base of this cylinder is a circle of radius ; its area measures out to:

The height of the cylinder is:

The volume of the cylinder measures out to:

Now try it using calculus:

When you look at the plotting instructions, you see that the points
       
with , , and
describe the cylinder and everything inside it.  This tells you that the volume of this cylinder measures out to
       :

Same as you got without calculus.